Response of soil carbon, nitrogen and phosphorus stoichiometric characteristics of Pinus tabuliformis forests to stand age and density in the Loess Plateau region of western Shanxi Province, northern China
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摘要:目的
分析油松林土壤碳（C）氮（N）磷（P）计量特征对林龄和密度的响应，旨在探究不同林龄条件下密度对土壤化学计量的影响规律，为油松人工林可持续经营提供科学依据。
方法以晋西黄土区蔡家川流域内3种林龄（30、40、50 a）和3种密度（1 000 ~ 1 500株/hm2、2 500 ~ 3 000株/hm2、4 000 ~ 4 500株/hm2）的油松人工林为研究对象，测定并分析0 ~ 100 cm土壤化学计量特征。
结果（1）林龄和密度的双因素交互作用对土壤有机碳（SOC）、土壤全氮（TN）、C∶N、C∶P、N∶P影响显著（P < 0.05）。（2）林龄对不同密度油松林土壤TN、SOC和化学计量比有不同影响，高密度林分中，在林龄增长至50 a时，表层土壤肥力指标出现明显衰退趋势；林龄较高时，低密度的林分土壤养分较高。（3）土壤TN 与 TP、SOC、C∶P、N∶P 均呈显著正相关（P < 0.05），SOC 与 C∶N、C∶P、N∶P均有极显著正相关关系（P < 0.01），C、N元素对林分生长指标有显著影响（P < 0.05）。
结论在黄土区应根据不同林龄阶段合理调节林分密度，30 a的油松林适宜密度为4 000株/hm2，40 a时密度应调整至2 500 ~ 3 000株/hm2，50 a的油松密度为1 000 ~ 1 500株/hm2时土壤养分最优。适宜的林分密度可以保证林地土壤养分状况维持在最优状态，有利于人工林分现阶段可持续经营以及后续土壤保育功能的持续发挥。
Abstract:ObjectiveAnalyzing the responses of soil carbon (C), nitrogen (N), and phosphorus (P) stoichiometry to stand age and density in Pinus tabuliformis forest land can provide scientific evidence for sustainable management of Pinus tabuliformis plantations.
MethodThis study focused on Pinus tabuliformis plantations of three stand ages (30, 40 and 50 years) and three densities (1 000−1 500 tree/ha, 2 500−3 000 tree/ha, 4 000−4 500 tree/ha) in the Caijiachuan Watershed, western Shanxi Province of northern China. Soil C, N, and P contents and their stoichiometric ratios were measured and analyzed from 0 to 100 cm depth layer.
ResultThe two-factor interaction of stand age and density showed a significant influence on SOC, total N (TN), C∶N, C∶P, and N∶P （P < 0.05). (2) Stand age had different effects on soil TN, SOC, and chemical stoichiometric ratios in stands of different densities, plantations with high density exhibited soil fertility decline at 50 years. Older plantations indicate that lower stand density is associated with higher soil nutrient levels. (3) Soil TN was significantly positively correlated with TP, SOC, C∶P, and N∶P (P < 0.05); SOC was significantly positively correlated with C∶N, C∶P, and N∶P (P < 0.01). C and N elements had a significant impact on soil chemical stoichiometry and stand growth (P < 0.05).
ConclusionIn loess area, it is necessary to rationally adjust stand density according to different Pinus tabuliformis stand ages. For a 30-year-old stand, the recommended density was 4 000 tree/ha. The density should be reduced to 2 500−3 000 tree/ha at 40 years. For a 50-year-old stand, the optimal density range for soil nutrients was 1 000−1 500 tree/ha. The appropriate stand density can ensure that the soil nutrient status of the forest land is maintained at an optimal level, which is beneficial for the current sustainable management of the artificial forest and the continuous function of subsequent soil conservation.
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现如今城市居住空间紧张，小户型的比例在逐渐加大。中国政府出台规定建筑面积90平方米以下户型占比必须达到70%以上[1]，这预示着更多的家庭面临功能空间不足的情况，就有大量家庭有一房两用的需求，即一个房间除了卧室的主要功能外，还可通过功能家具实现客厅或书房等功能，而其中翻转床则是实现睡眠–休闲、学习空间转换的功能家具的典型代表产品。
虽然翻转床有着可观的市场需求，但对于其力学性能的检测还是依赖整体破坏性试验为主要手段，目前其设计和分析尚缺乏科学的理论指导[2]。20世纪90年代气弹簧作为新型支撑出现，张琦等[3]对气弹簧的力学性能进行了计算分析；王殿武[4]研究了气弹簧力学特性并将其运用到汽车尾盖上；刘迎林等[5]对全塑车身后备箱气撑杆进行运动仿真并验证其安装位置；王定虎[6]运用力矩平衡原理和理想气体方程对汽车背门撑杆的选择及布置进行校核。截止目前，气弹簧的研究主要集中在汽车领域，而鲜有在家具领域内的研究，为了弥补翻转床气弹簧机构设计和性能分析的理论欠缺，本文从实际应用需求出发，运用静力学和力矩平衡原理对气弹簧机构进行结构分析计算和选型。
1. 研究方法
1.1 翻转床气弹簧机构概况
翻转床床体翻转的目的是实现床体的收纳，以便满足房间睡眠–休闲、学习空间转换的用户功能需求。根据使用场景分析，翻转床运动功能示意图如图1所示。因为翻转床的床体框架、床板、床垫和床上用品等零部件加起来质量较大，如仅凭借人手部力量支撑则翻转困难，且在操作过程中存在砸到人的风险，所以实际翻转床产品均需要借助辅助结构实现翻转和随停的功能。由于气弹簧具有支撑、缓冲的作用，因此恰好适用于翻转床的运动功能需求。
壁柜式翻转床的翻转功能主要由气弹簧机构实现，分析翻转床的运动本质就是分析气弹簧机构。壁柜式翻转床结构和气弹簧机构简图如图2所示，翻转床左右两侧具有相同连杆结构，其中A点为翻转床的翻转中心，由螺栓将床体翻转框架和固定柜体铰接；BC为气弹簧，气弹簧两端分别和固定柜体及床体翻转框架铰接；床体翻转存在两个极限状态，即收纳状态（图2a）和使用状态（图2b），处于收纳状态时气弹簧处在伸展状态，即B1C，处于使用状态时气弹簧处在压缩状态，即BC。
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图 2 翻转床结构和气弹簧机构简图1. 固定柜体；2. 气弹簧；3. 床体翻转框架；A. 翻转中心；B. 气弹簧压缩末端；B1. 气弹簧伸展末端；C. 气弹簧固定端; l. A点到床头距离。 1, fixed cabinet; 2, gas spring; 3, rotate frame; A, rotation center; B, compression end of gas spring; B1, stretching end of gas spring; C, fixed end of gas spring; l, the distance from A point to the head of the bed.Figure 2. Diagram of foldable bed structure and gas spring mechanism1.2 气弹簧计算方法
根据国家标准GB 25751—2010压缩气弹簧技术条件、GB/T 1805—2001弹簧术语和JB/T 10418—2004气弹簧设计计算为依据，对气弹簧特性进行研究。对极限位置的床体进行平面力系的简化，并结合力矩平衡原理对床体和气弹簧机构进行受力分析。运用有限元的优化思路对气弹簧安装位置进行列表格寻最优解。运用静力学知识分析床体运动规律。
2. 结果与分析
2.1 气弹簧机构分析计算和选型
如图2所示，翻转床在收纳时气弹簧处于伸展过程，气弹簧的伸展力辅助床体的上翻过程。床体完全收纳进柜体时，此时床体重力矢量经过翻转中心A，在无外力情况下床体静止不动。翻转床展开过程中气弹簧处于压缩过程，气弹簧的压缩力为床体下翻过程提供缓冲力。
图3为气弹簧展开长度与压缩、伸展过程曲线示意图，其中F1为最小伸展力，F2为最大伸展力，F3为最小压缩力，F4为最大压缩力，S为气弹簧的行程，t为端头长度，结合图2气弹簧初始长度BC = S + t，展开长度L = B1C = S + t + S = 2S + t，t的取值一般为10 mm。
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图 3 气弹簧展开长度与压缩、伸展过程曲线示意图d. 活塞杆直径；D1. 缸筒内径；D2. 缸筒外径；S. 行程；L. 伸展长度；t. 端头长度；F0. 启动力；F1. 最小伸展力；F2. 最大伸展力；F3. 最小压缩力；F4. 最大压缩力；Fa. 公称力a；Fb. 公称力b；C. 采力点。图引自文献[7]。d, piston rod diameter; D1, cylinder inner diameter; D2, cylinder outer diameter; S, stroke; L, extended length; t, end length; F0, star-up force; F1, minimum extension force; F2, maximum extension force; F3, minimum compress force; F4, maximum compress force; Fa, nominal force a; Fb, nominal force b; C, measuring point. Diagram is cited from reference [7].Figure 3. Diagram of expansion length of gas spring and curve of compression and stretching process气弹簧的选型需要的参数为气弹簧的伸展长度L和行程S以及气弹簧最小伸展力F1[8]。现以翻转床两个极限位置进行受力分析。使用状态下，当人手抬起床的边沿时以A点为旋转中心，能够将床体抬起。此时受力分析如图4所示。
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图 4 使用状态手抬床体时床体受力分析简图A. 翻转中心；B. 气弹簧压缩末端；C. 气弹簧固定端；F2. 气弹簧最大伸展力；G1. A点左侧床体质量与重力加速度之积；G2. A点右侧床体质量与重力加速度之积；FAx. A点沿x轴方向分力；FAy. A点沿y轴方向分力；l. A点到床头距离；FL. 手对床体的抬力；A, rotation center；B, compression end of gas spring；C, fixed end of gas spring；F2, maximum extension force；G1, bed weight on the left side of point A；G2, bed weight on the right side of point A；FAx, x component of point A；FAy, y component of point A；l, A point to the head of the bed；FL, hand lift on the bed.Figure 4. Diagram of foldable bed force analysis when hand up the bed in using state由力矩平衡可得：
xF2l+G1l2−G2LB−l2+FL(LB−l)=0 (1) 式中：F2为气弹簧最大伸展力，单位N；x为气弹簧个数；FL为手对床体的抬力，单位N；LB为床体总长，单位mm；G1为A点左侧床体质量与重力加速度之积，单位N；G2为A点右侧床体质量与重力加速度之积，单位N；l为A点到床头距离，单位mm。
设床体和床垫总质量为m，
G1=lLBmg ，G2= LB−lLBmg ，则可将式（1）简化得：xF2l−(LB2−l)mg+FL(LB−l)=0 (2) 式中：F2为气弹簧最大伸展力，单位N；x为气弹簧个数；FL为手对床体的抬力，单位N；LB为床体总长，单位mm；l为A点到床头距离，单位mm；m为床体和床垫总质量，单位kg；g为重力加速度，单位N/kg。
收纳状态下，拉手与A、B1点视作在同一竖直线上。拉动床体时，人手拉动拉手的力矩能够平衡气弹簧对A点的弹力矩，此时受力分析简图如图5所示。
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图 5 收纳状态手拉床体时床体受力分析简图A. 翻转中心；B1. 气弹簧伸展末端；C. 气弹簧固定端；FAx. A点沿x轴方向分力；FAy. A点沿y轴方向分力；F0. 启动力；F0x. F0沿x轴方向分力；F0y. F0沿y轴方向分力；l. A点到床头距离；θ. F0与垂直方向夹角；FP. 手对拉手拉力。A, rotation center；B1, stretching end of gas spring；C, fixed end of gas spring；FAx, x component of point A；FAy, y component of point A； F0, star-up force; F0x, x component of F0; F0y. y component of F0; l, A point to the head of the bed; θ, angle of F0 with vertical direction; FP, hand pull on the handle.Figure 5. Diagram of foldable bed force analysis when hand drag the bed in storage state因为F0y与A点在水平方向上没有距离，所以F0在y轴方向上的力矩为0。由力矩平衡可得：
x(F0xl+F0y⋅0)−FP(lP−l)=0 (3) 式中：F0为气弹簧启动力，单位N；lP为拉手高度，单位mm；FP为手对拉手拉力，单位N；l为A点到床头距离，单位mm；x为气弹簧个数；F0x为F0沿x轴方向分力，单位N；F0y为F0沿y轴方向分力，单位N。
图5中，依据压缩气弹簧技术条件，气弹簧启动力F0略大于气弹簧最小压缩力F3，取F3值近似为F0值，由三角函数可知：
F0=F0xsinθ=F3 (4) 式中：θ为F0与垂直方向夹角，单位°；F0为气弹簧启动力，单位N；F0x为F0沿x轴方向分力，单位N；F3为气弹簧最小压缩力，单位N。
在符合人机工程的情况下，使lP尽量大可以加大手拉开床体的力矩，减小手部力量，取lP = 1 750 mm。依据人机工程学，为使得操作力比较恰当，收纳床体时推荐的操作力范围为50 ~ 80 N[9]，此处取手对床体的抬力FL = 80 N，手拉拉手的力FP = 80 N。
F1与F3之间有一段由于摩擦力产生的差值，依据GB25751—2010其计算公式为Fr =（F3 − F1）/2，即动态摩擦力Fr是最小压缩力和最小伸展力之差的平均值[10]。气弹簧摩擦力所产生的阻力与杆的运动方向相反，其与标称力值（图样及产品上标注的力，包括F1、Fa、
F3⋯⋯ ）极限偏差应符合下表1的规定。表 1 标称力值极限偏差与动态摩擦力Table 1. Nominal force limit deviation and dynamic friction标称力值 Nominal force 标称力值的极限偏差 Nominal force limit deviation 最大动态摩擦力 Maximum dynamic friction ≤ 100 + 15 − 5 25 101 ~ 200 + 20 − 10 30 201 ~ 400 + 30 − 15 40 401 ~ 600 + 40 − 20 60 601 ~ 800 + 50 − 25 80 801 ~ 1 000 + 60 − 30 100 1 001 ~ 1 200 + 70 − 35 130 > 1 200 + 80 − 40 150 注：表1引自文献[7]。Note: Tab.1 is cited from reference [7]. F1与F2的关系可由弹性系数求得。弹性系数k表示的是单位压缩力变化的弹簧常数[10]，单位为N/mm，行程S的单位是mm。伸展阶段气弹簧弹性系数公式[11]为：
k=(F2−F1)/S (5) 其中，k的大小可由厂家进行调节，其具体值可通过实验得出。一般商家提供的气弹簧的弹性系数k介于1.05和1.8之间，弹性系数越小意味着制造难度越高。
以市场常见的床体规格为准，此处选取宽900 mm、长1 900 mm、质量为25 kg的床垫。选取匹配的床体框架结构的材质为钢，其质量约为25 kg。刨花板密度为650 kg/m3，则18 mm（厚） × 900 mm（宽） × 1 900 mm（长）的床板质量为20 kg。则床体总重力为：（25 + 25 + 20） × 9.8 = 686 N。如固定柜体目标深度为300 mm，为了保证A、C两点安装位置距离柜体板前后两边有足够的距离保证强度，则取l = 160 mm。
依据式（2），xF2 = 2 517.1 N，选取气弹簧个数x = 4，则F2 = 629.3 N。
由图4、图5可知：取l为160 mm时，以B、B1为圆心，以（S + 10）、（2S + 10）为半径作圆，作交点可得C点安装位置。并结合式（3）、式（4）、表1以及k的计算方程，可将相关参数整理成表2。
表 2 气弹簧相关参数及安装位置与行程S的关系Table 2. Relationship between gas spring stroke and relevant parameters and installation positionS/mm θ/° F3/N Fr/N F1/N k 170 18 643.2 180 20 581.1 60 461.1 0.934 190 23 508.0 40 428.0 1.059 200 26 453.4 40 373.4 1.280 注：S为行程；θ为F0与垂直方向夹角；F3为最小压缩力；Fr为最大动态摩擦力；F1为最小伸展力；k为气弹簧弹性系数。表3同此。Notes：S, stroke; θ, angle of F0 with vertical direction; F3, minimum compress force; Fr, maximum dynamic friction; F1, minimum extension force; k, gas spring modulus coefficient. Same as Tab.3. 由表2可知：θ角越大，k则越大，气弹簧的制作难度越小。为减小安装宽度，选择S为190 mm，F1 = 428 N作为最小伸展力的气弹簧，则要求厂家提供的气弹簧弹性系数k为1.06。参考表3可知F1和S的参数符合设计要求。
表 3 气弹簧活塞杆直径与最小伸展力大小选择范围推荐表Table 3. Recommended table of minimum extension force range and stroke range of gas spring序号
No.活塞杆
直径 Diameter of piston rod/mm最小伸展力
Minimum extension force (F1)/N行程范围
Stroke range/mm推荐范围
Recommended
range可选范围
Optional
range1 6 50 ~ 250 50 ~ 350 50 ~ 400 2 8 200 ~ 450 100 ~ 700 100 ~ 700 3 10 300 ~ 700 100 ~ 1 200 150 ~ 1 100 4 12 450 ~ 1 000 150 ~ 1 500 150 ~ 1 600 5 14 600 ~ 1 400 200 ~ 2 500 1 600 ~ 2 200 6 20 1 250 ~ 3 100 1 000 ~ 5 200 2 200 ~ 4 500 注：表3引自文献[12]。Note: Tab.3 is cited from reference [12]. 此时C点的安装位置如图6所示，BC = S + 10 = 200 mm，B1C = 2S + 10 = 390 mm。如果床体总质量加大，可以适当改变固定柜体深度以加大l的取值，使气弹簧机构获得更大的力臂。
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图 6 C点安装位置示意图A. 翻转中心；B. 气弹簧压缩末端；B1. 气弹簧伸展末端；C. 气弹簧固定端。A, rotation center; B, compression end of gas spring; B1, stretching end of gas spring; C, fixed end of gas spring.Figure 6. Diagram of installation location of point C2.2 翻转床运动规律分析
翻转床旋转到任意角度时的受力图如图7所示。取气弹簧对床体弹力FB与矩心A点的力臂为a，G1与矩心A点的力臂为b，G2与矩心A点的力臂为c。矩心A点右侧力矩减去左侧合力矩可列式：
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图 7 任意位置下床架受力图A. 翻转中心；B′. 在β旋转角度下的床尾位置；C. 气弹簧固定端；β. 床体翻转框架翻转角度；G1. A点左侧床体质量与重力加速度之积；G2. A点右侧床体质量与重力加速度之积；a. FB对矩心A点的力臂；b. G1对矩心A点的力臂；c. G2对矩心A点的力臂。A, rotation center; B′, bed tail position at β rotation angle; C, fixed end of gas spring; β, flip angle of rotate frame; G1, bed mass on the left side of point A multiply gravity acceleration; G2, bed mass on the right side of point A multiply gravity acceleration; a, FB force arm to point A; b, G1 force arm to point A; c, G2 force arm to point A.Figure 7. Diagram of foldable bed force at arbitrary degreeMA=MA(xFB)+MA(G1)−MA(G2)=xFBa+G1b−G2c (6) 式中：MA为合力对A点的力矩，单位N；x为气弹簧个数；FB为气弹簧对床体弹力，单位N；G1为A点左侧床体重力，单位N；G2为A点右侧床体重力，单位N；a为FB对矩心A点的力臂，单位mm；b为G1对矩心A点的力臂，单位mm；c为G2对矩心A点的力臂，单位mm；MA（xFB）为单边气弹簧对A点力矩，单位N·mm；MA（G1）为G1对A点力矩，单位N·mm；MA（G2）为G2对A点力矩，单位N·mm。
气弹簧压缩和伸展两个过程曲线中任意点的值可以用伸展长度和k值求出，在不同旋转角度β下分别量取a、b、c的值代入式（6），并作出β与MA的关系曲线如图8所示。图8两条曲线为分别代入了弹簧伸展过程力值和压缩过程力值后的曲线。由图 8可知：床体在打开18°以内会弹回收纳状态；18° ~ 24°之间床体可悬停；大于24°以后，A点右侧力矩大于A点左侧合力矩。
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图 8 β与MA关系曲线MA. 合力对A点的力矩；β. 床体翻转框架翻转角度。MA, torque to point A；β, flip angle of rotate frame.Figure 8. Diagram of β and MA curve3. 结 论
基于静力学和力矩平衡原理完成了翻转床两个极限位置的受力分析，构建了翻转床气弹簧分析计算理论，运用该理论能够通过翻转床的床身质量和尺寸得到气弹簧的最小伸展力、行程和弹性系数，从而完成气弹簧选型；运用CAD工具做两圆相交的几何法得出气弹簧安装位置的确立方法；基于力矩平衡原理构建合力矩和翻转角度β的关系式，得出翻转床悬停范围。设定床体尺寸宽900 mm、长1 900 m、固定柜体目标深度300 mm，则可得气弹簧最小伸展力为428 N，行程为190 mm，弹性系数为1.06，悬停角度范围为18° ~ 24°，翻转角大于24°后则为自由下翻。本文构建的分析方法和结果可为家具行业的壁柜式翻转床设计、选型和性能分析提供理论支撑和实践指导。
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图 2 不同林龄和密度油松林0 ~ 100 cm土壤养分含量
不同大写字母表示相同林龄，不同密度之间差异显著（P < 0.05）；不同小写字母表示相同密度，不同林龄之间差异显著（P < 0.05）。下同。Different capital letters indicate significant differences (P < 0.05) between varied densities of the same stand age, and different lowercase letters indicate significant differences (P < 0.05) between varied stand ages of the same density. Same as below.
Figure 2. Nutrient contents of 0−100 cm soil of different stand ages and densities of Pinus tabuliformis plantation
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图 3 不同林龄、密度油松林地0 ~ 100 cm分层土壤养分含量
Figure 3. Nutrient contents in different soil layers of 0−100 cm of Pinus tabuliformis plantation with different stand ages and densities
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图 4 不同林龄和密度油松林0 ~ 100 cm土壤化学计量比
Figure 4. Stoichiometric ratios of 0−100 cm soil of different stand ages and densities of Pinus tabuliformis plantation
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图 5 不同林龄、密度油松林地0 ~ 100 cm土壤化学计量比
Figure 5. Stoichiometric ratios in different soil layer of 0−100 cm of Pinus tabuliformis plantation with different stand ages and densities
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图 6 油松人工林地土壤 C、N、P含量、化学计量比与林分生长的相关性分析
DBH. 胸径；H. 树高；V. 单木材积；M. 林分蓄积量。DBH, diameter at breast height; H, tree height; V, single tree volume; M, stand volume.
Figure 6. Correlation analysis of soil C, N and P contents, stoichiometric ratios and growth of Pinus tabuliformis plantation
表 1 样地基本情况
Table 1 Basic information of sample plots
林分类型
Stand type林龄/a
Stand
age/year林分密度/（株·hm−2）
Stand density/
（tree·ha−1）坡度
Slope/（°）海拔
Altitude/m平均胸径
Average
DBH/cm平均树高
Average tree
height/m单木材积
Single tree
volume/m3林分蓄积量/（m3·hm−2）
Stand volume/
（m3·ha−1）YD 30 1 125 34 1 189 14.55 8.33 0.24 271.72 1 025 28 1 139 14.13 7.52 0.19 203.53 1 250 30 1 158 14.04 8.22 0.22 279.98 YZ 2 650 30 1 075 10.98 8.67 0.15 410.43 2 875 27 1 171 12.86 9.79 0.23 674.33 2 800 30 1 196 11.82 7.85 0.14 417.56 YG 4 475 36 1 252 10.67 10.12 0.18 846.17 4 000 29 1 290 10.92 9.19 0.16 671.92 4 100 20 1 357 9.48 8.15 0.11 467.55 ZD 40 1 266 38 1 350 13.65 8.87 0.22 280.74 1 175 36 1 403 14.37 9.47 0.28 337.77 1 475 28 1 367 15.30 11.15 0.40 600.23 ZZ 2 875 34 1 340 9.03 6.44 0.07 213.89 2 900 26 1 358 12.70 10.28 0.24 719.19 2 788 22 1 370 11.90 10.13 0.22 615.55 ZG 4 200 22 1 279 10.60 8.27 0.13 575.26 4 500 24 1 339 10.11 7.03 0.10 451.04 4 425 30 1 366 8.84 6.76 0.07 342.94 LD 50 1 200 21 1 372 14.66 8.01 0.23 276.94 1 375 25 1 385 14.21 10.11 0.31 430.48 1 500 25 1 390 14.63 10.36 0.33 509.22 LZ 2 975 30 1 336 11.87 10.16 0.22 657.48 3 000 21 1 333 10.94 7.37 0.12 362.91 2 600 25 1 354 13.27 9.72 0.24 631.99 LG 4 000 31 1 199 9.84 6.12 0.07 314.71 4 025 21 1 307 11.02 10.47 0.20 840.07 4 088 20 1 344 11.37 8.98 0.17 702.65 注：林分类型中字母Y、Z、L分别代表30、40、50 a 3种林龄；字母D、Z、G分别代表低（1 000 ~ 1 500株/hm2）、中（2 500 ~ 3 000株/hm2）、高（4 000 ~ 4 500株/hm2）3种密度。Notes: letters Y, Z, and L in stand type represent 30, 40, and 50 years, respectively; and the letters D, Z, and G represent low (1 000−1 500 tree/ha), medium (2 500−3 000 tree/ha), and high (4 000−4 500 tree/ha) densities, respectively. 
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表 2 油松人工林地土壤 C、N、P含量及化学计量比的多因素方差分析
Table 2 Multi-way ANOVA of soil C, N and P contents and stoichiometric ratios of Pinus tabuliformis plantation
因素
Factor土壤有机碳含量
Soil organic
carbon (SOC) content全氮含量
Total nitrogen
(TN) content全磷含量
Total phosphorus
(TP) content土壤碳氮比
Soil C∶N土壤碳磷比
Soil C∶P土壤氮磷比
Soil N∶P林龄 Stand age 20.32** 1.32* 1.28 42.95** 29.01** 3.83* 密度 Density 4.67* 3.27* 0.97 5.64** 3.32* 3.70* 土层深度 Depth of soil layer 65.63** 35.99** 0.27 1.28 62.48** 39.80** 林龄 × 密度 Stand age × density 6.01** 1.98* 1.22 5.45** 7.32** 3.55** 林龄 × 土层深度 Stand age × depth of soil layer 1.59 0.72 0.34 0.37 1.86 0.94 密度 × 土层深度 Density × depth of soil layer 0.83 0.61 0.36 0.35 0.56 0.55 林龄 × 密度 × 土层深度
Stand age × density × depth of soil layer0.79 0.78 0.34 0.52 1.07 0.98 注：*、**分别代表在P < 0.05、P < 0.01水平上显著相关。下同。表中数字为F值。Notes：* and ** represent significant correlations at level of P < 0.05 and P < 0.01, respectively. Same as below. The numbers in the table are F values.
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